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SSC Pure Mathematics QUESTION #11191
Question 1
Projection of $\mathbf{a}$ on $\mathbf{b}$ is:
  • $\mathbf{a}\cdot\mathbf{b}$
  • $\dfrac{\mathbf{a}}{|\mathbf{a}|}\cdot\mathbf{b}$
  • $\mathbf{a}\cdot\dfrac{\mathbf{b}}{|\mathbf{b}|}$✔️
  • $\mathbf{a}\times\mathbf{b}$
Correct Answer Explanation
The scalar projection of $\mathbf{a}$ onto $\mathbf{b}$ is $\mathbf{a}\cdot\hat{\mathbf{b}} = \mathbf{a}\cdot\dfrac{\mathbf{b}}{|\mathbf{b}|}$. This gives the component of $\mathbf{a}$ in the direction of $\mathbf{b}$, equal to $|\mathbf{a}|\cos\theta$ where $\theta$ is the angle between the vectors.